• numerals represent ETs (steps per '2')
• multiple appearances of the same number are different mappings
• rotation of the ET numbers indicates octave stretch of the TOP tuning of the ET (15 cents stretch = 90° clockwise rotation)
• lines are temperaments (where a single comma is tempered out)
• hexagons are contours of maximum Tenney-weighted damage of TOP tunings

5-limit

{2,3,5} PTS with handwritten annotations from A Middle Path

Paul Erlich > ‎The Xenharmonic Alliance (2011-02-04) projective tuning space based on {2,3,5} numerals at ETs represent steps per '2' hexagons are contours of maximum Tenney-weighted damage of TOP tunings

	Paul Erlich > ‎The Xenharmonic Alliance - Mathematical Theory (2014-08-22) zoomed waaaay out
	Paul Erlich > ‎The Xenharmonic Alliance - Mathematical Theory (2014-08-22) zoomed-out still more
	Paul Erlich > ‎The Xenharmonic Alliance - Mathematical Theory (2014-08-22) zoomed-out more
	Paul Erlich > ‎The Xenharmonic Alliance - Mathematical Theory (2014-08-22) zoomed-out
	Paul Erlich > ‎The Xenharmonic Alliance - Mathematical Theory (2014-04-10) 5-limit projective tuning space showing equal temperaments and good rank-two temperaments (or "temperament families"). Concentric hexagons indicate TOP damage (of TOP tuning) up to 10 in increments of 1.
	Paul Erlich > ‎The Xenharmonic Alliance - Mathematical Theory (2014-08-25) zoomed-in
	Paul Erlich > ‎The Xenharmonic Alliance - Mathematical Theory (2014-08-25) zoomed-in more
	Paul Erlich > ‎The Xenharmonic Alliance - Mathematical Theory (2014-08-25) zoomed-in still more
	Paul Erlich > ‎The Xenharmonic Alliance - Mathematical Theory (2014-08-25) zoomed way in
	Paul Erlich > ‎The Xenharmonic Alliance - Mathematical Theory (2014-08-25) zoomed way way in

	Paul Erlich > ‎The Xenharmonic Alliance - Mathematical Theory (2014-08-26) showing all three elements of each 5-limit breed zoom level 0
	Paul Erlich > ‎The Xenharmonic Alliance - Mathematical Theory (2014-08-26) showing all three elements of each 5-limit breed zoom level 1
	Paul Erlich > ‎The Xenharmonic Alliance - Mathematical Theory (2014-08-26) showing all three elements of each 5-limit breed zoom level 2
	Paul Erlich > ‎The Xenharmonic Alliance - Mathematical Theory (2014-08-26) showing all three elements of each 5-limit breed zoom level 3
	Paul Erlich > ‎The Xenharmonic Alliance - Mathematical Theory (2014-08-26) showing all three elements of each 5-limit breed zoom level 4
	Paul Erlich > ‎The Xenharmonic Alliance - Mathematical Theory (2014-08-26) showing all three elements of each 5-limit breed zoom level 5
	Paul Erlich > ‎The Xenharmonic Alliance - Mathematical Theory (2014-08-26) showing all three elements of each 5-limit breed zoom level 6
	Paul Erlich > ‎The Xenharmonic Alliance - Mathematical Theory (2014-08-26) showing all three elements of each 5-limit breed zoom level 7

11-limit subgroups

	Paul Erlich > ‎The Xenharmonic Alliance (2011-02-04) projective tuning space based on {2,3,7} numerals at ETs represent steps per '2' hexagons are contours of maximum Tenney-weighted damage of TOP tunings
	Paul Erlich > ‎The Xenharmonic Alliance (2011-02-06) projective tuning space based on {2,3,7} zoomed way out!

Paul Erlich > ‎The Xenharmonic Alliance (2011-02-06) "projective tuning space" "based on" "{2,3,9}" numerals at "ETs" represent steps per '2' hexagons are "contours" of "maximum Tenney-weighted damage" of "TOP tunings" this one is not like the others! 9/3 is considered a different interval than 3, with complexity log(27) rather than log(3), and susceptibility to damage 1/log(27) instead of 1/log(3) -- whatever that means!

Paul Erlich > ‎The Xenharmonic Alliance (2011-02-06) projective tuning space based on {2,3,11} numerals at ETs represent steps per '2' hexagons are contours of maximum Tenney-weighted damage of TOP tunings

Paul Erlich > ‎The Xenharmonic Alliance (2011-02-04) projective tuning space based on {2,5,7} numerals at ETs represent steps per '2' hexagons are contours of maximum Tenney-weighted damage of TOP tunings

Paul Erlich > ‎The Xenharmonic Alliance (2011-02-06) projective tuning space based on {2,5,9} numerals at ETs represent steps per '2' hexagons are contours of maximum Tenney-weighted damage of TOP tunings

Paul Erlich > ‎The Xenharmonic Alliance (2011-02-06) projective tuning space based on {2,5,11} numerals at ETs represent steps per '2' hexagons are contours of maximum Tenney-weighted damage of TOP tunings

Paul Erlich > ‎The Xenharmonic Alliance (2011-02-06) projective tuning space based on {2,7,9} numerals at ETs represent steps per '2' hexagons are contours of maximum Tenney-weighted damage of TOP tunings

Paul Erlich > ‎The Xenharmonic Alliance (2011-02-06) projective tuning space based on {2,7,11} numerals at ETs represent steps per '2' hexagons are contours of maximum Tenney-weighted damage of TOP tunings

Paul Erlich > ‎The Xenharmonic Alliance (2011-02-06) projective tuning space based on {2,9,11} numerals at ETs represent steps per '2' hexagons are contours of maximum Tenney-weighted damage of TOP tunings

3.5.7, tritave (3-1) based

Paul Erlich > ‎The Xenharmonic Alliance (2011-02-04) projective tuning space based on {3,5,7} numerals at ETs represent steps per '3' hexagons are contours of maximum Tenney-weighted damage of TOP tunings